theorem
  seq is convergent implies lim (seq - x) = (lim seq) - x
proof
  assume seq is convergent;
  then lim (seq + (-x)) = (lim seq) + (-x) by Th17;
  then lim (seq - x) = (lim seq) + (-x) by BHSP_1:56;
  hence thesis by RLVECT_1:def 11;
end;
